层状横观各向同性饱和土的非轴对称动力响应

THE NON-AXISYMMETICAL DYNAMIC RESPONSE OF LAYERED TRANSVERSELY ISOTROPIC SATURATED SOILS

通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的Biot非轴对称波动方程转化为一组一阶常微分方程组.然后基于径向Hankel变换,建立问题的状态方程;求解状态方程后,得到传递矩阵.进而利用传递矩阵,结合饱和层状地基的边界条件、排水条件及层间接触和连续条件,求解了任意震源力作用下层状横观各向同性饱和地基频域动力响应问题.时域解可通过频率的Fourier积分得到.

The dynamic response of layered saturated soils to an arbitrary buried source is useful and important in seismology, seismic engineering, soil mechanics, geophysics, dynamic foundation theory and so on. Therefore, after Biot putting forward the general wave equations in isotropic saturated porous medium, there are a series of work on dynamic response in such medium by the FEM, BEM(in frequency space or Laplace space), as well as analytical method(completed by Fourier expanding and Hankel integral transformation). However, the most researches focus on the isotropic saturated porous medium less involving in anisotropic medium and existing the limitations among the work mentioned above: the FEM relating to enormous amount of calculation as well as complex artificial boundary, the BEM involving in the completed dynamic singular close solution, which is hard to attain in layered saturated porous medium. Although the analytical expression in dynamic stiffness matrix containing 8(N + 1) pending coefficients is given in Ref.[10], it is an onerous work for computing N-layers saturated soils.The purpose of this article is to study the non-axisymmetical dynamic response of layered transversely isotropic saturated soils under an arbitrary buried source. In the first part, based on Biot's theory for fluid-saturated porous media, the 3-D wave equations in cylindrical coordinate for transversely isotropic saturated poroelastic media are transformed into the 1-order governing differential equations completed by the Fourier expanding with respect to azimuth. Then, transfer matrixes within layered media are derived by introducing combined state vector and Hankel integral transformation. The second part gives the analytical expression in dynamic response for multilayered such medium using transfer matrixes followed by boundary conditions and continuity conditions as well as drainage conditions. In the third part, some numerical results are listed. Time-domain results may obtain by Fourier synthesis over frequency.